Per the challenge Brief, "the issue is not 'what resources to provide' but 'how to get the resources to the people who need them most.'” My idea here works for most/all existing resources, by making sure that pet owners can easily FIND INFORMATION about those resources, and especially the resources available in their communities. This is accomplished through a non-judgemental CHATBOT conversing with pet owners via texting, online chat, phone call, etc, and directing them to the right resources.
When life circumstances affect a person’s ability to care for (support) their pets, often the person goes through various phases, e.g. denial, anger, self-pity, depression, etc, before acceptance sets in - that he/she needs help with his/her pets. This delay is one problem. Another is the person's reluctance to share his concerns with a known person. Today high phone/internet penetration mean there are less barriers to accessing the bot (and to real human counselors, if a pet owner requests so).
Print/online/SEO/radio/local/shelter/vets/retailers etc channels shall publicize the bot. E.g., on each pet food purchase receipt, print: "Pet helpline @4PetHelp 833-4PETHELP"
Pet owners, who might otherwise be reticent about discussing issues with a live person, can thus seek and obtain information and/or referrals through the AI-driven chatbot. The bot shall tailor its information to the type of pet, location, the pet owner's financial/housing/employment/immigration constraints, etc.